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On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation

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  • Papageorgiou, Nikolaos S.

Abstract

Banach space valued multifunctions defined on a complete [sigma]-finite measure space ([Omega], [Sigma], [mu]) are studied. Their set valued integral is defined and its properties are examined. Since the definition of the integral involves the set of integrable selectors of the multifunction, the structure of that set is also studied. Some Banach-like spaces of multifunctions are introduced and studied. Multifunctions depending on a parameter are also considered and it is examined wheter certain continuity, semicontinuity and other topological properties are preserved by set valued integration. Finally, for integrable multifunctions, the properties of their set valued conditional expectation are studied.

Suggested Citation

  • Papageorgiou, Nikolaos S., 1985. "On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 185-206, October.
    • Handle: RePEc:eee:jmvana:v:17:y:1985:i:2:p:185-206
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    Cited by:

    1. M. Guo & X. Xue & R. Li, 2004. "Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 355-374, February.
    2. Daniel Ralph & Huifu Xu, 2011. "Convergence of Stationary Points of Sample Average Two-Stage Stochastic Programs: A Generalized Equation Approach," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 568-592, August.
    3. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    4. Hailin Sun & Huifu Xu & Yong Wang, 2014. "Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via Conditional Value at Risk and Difference of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 257-284, April.
    5. Huifu Xu & Dali Zhang, 2013. "Stochastic Nash equilibrium problems: sample average approximation and applications," Computational Optimization and Applications, Springer, vol. 55(3), pages 597-645, July.
    6. Wei Ouyang & Kui Mei, 2023. "Quantitative Stability of Optimization Problems with Stochastic Constraints," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
    7. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.

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